re: I'll ask this on this board: LOTR, Saruman

Saruman COULD do this, and he COULD make his own Ring, totally independent of Sauron's.

You have to consider the background of the Maia at play here.

Arda, the World (Universe), was created empty by Eru. The Ainur (Valar and Maia) had to build it.

Short summary of the Maia in discussion: Sauron, Saruman, Gandalf, Radagast.

Sauron was a graduate of Aule School of Technology.
Gandalf, from Lorien School of Philosophy.
Radagast, from Yavannah School of Agriculture.

Saruman was ALSO from Aule Tech
He has the same training and education on how things are made, and how things work, that Sauron does.

Aule, being the Valar smith (Vulcan or Hephaestus basically), was the one that MADE stuff, and taught the Noldor (thus the Silmarils, the Palantirs etc), the Dwarves, etc.

Sauron, with his background education, knew there was a "magic" energy that could be tapped into, like 'the internet'. He knew that you could build devices that would use that magic (a computer), but you'd need a connection (a modem).
So he collaborated with Celebrimbor, and shared a lot of knowledge... but he did not teach Celebrimbor the principles about the access point in general. He only gave him a single access, which tied everything to the One Ring.
The One Ring was basically the modem or router. Celebrimbor was way over his head, building nice pc's maybe, but no matter what he did, it all was locked into Sauron's "wifi connection". That way, Sauron could control everything.
And that way, when the One Ring was unmade, all connections were lost.

Now, if you remember, there was discussions among the Wise about what would happen if the One were destroyed. Some thought the Three would be free, some thought the Three would stop working (as happened).

Saruman, being the Aule Tech grad, most certainly worked out the issue, and correctly understood that the One was the connection, and it it were unmade, all the current Rings would fail.
That's because he understood EXACTLY what they were, in concept.

He would understand that the device (a Ring) could work, but also understand that he'd have to start from scratch, and devise his own connection. He PROBABLY could make one near in quality to the Seven or Nine, but if he didn't do the necessary work, if he just copy-pasted the code used to make the existing ones, his ring would instantly connect to Sauron's LAN, and he'd be screwed. It's stated multiple times, he never intended to serve under Sauron, he wanted to independently take things over himself.

So if he had gotten to the point of making a ring, he'd have worked it out to where he made his own connection. Once that was done, the rest is simply improving the end-user aspect (making the rings 'stronger' or 'better', like getting a better CPU in a computer).